Let and be the two sets of observations. If and are their respective means and is the variance of all the observations in , then is equal to:

603 Explanation: Solution Step 1: Dono sets ka mean ( aur ) nikalna Dono sets Arithmetic Progression (AP) mein hain. AP ka mean middle term hota hai: Set ke liye numbers se tak hain ( ): Set ke liye numbers se tak hain ( ): Step 2: Combined Variance ( ) nikalna Combined set mein total observations hain. Pehle combined mean ( ) nikalte hain: Ab variance ka formula use karenge: . Lekin yahan ek shortcut formula behtar rahega: Dono sets consecutive integers hain, isliye dono ka individual variance same hoga: Ab values put karte hain: Step 3: Final Calculation Hame find karna hai : Answer: The value is 603 .

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $X = \{11, 12, 13, \dots, 40, 41\}$ and $Y = \{61, 62, 63, \dots, 90, 91\}$ be the two sets of observations. If $\bar{x}$ and $\bar{y}$ are their respective means and $\sigma^2$ is the variance of all the observations in $X \cup Y$ , then $|\bar{x} + \bar{y} - \sigma^2|$ is equal to:

JEE 2023 — Mathematics PYQ

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